There are those who propose that a spiral introduced within a volume within a speaker enclosure is no more than a fancy folding scheme with the disadvantage of being extremely complicated to design.
They will claim that a spiral will offer absolutely no benefit towards reducing the size of a bass speaker enclosure.

However, I would propose that those who partake of that view are neglecting to factor into their consideration the principle of acoustical induction.

Quoting from the above referenced link, consider the following quotes:

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Where are horns used, and for what?Throughout the history of electroa­coustics, there have been two important aspects:Loading of the driverDirectivity control

You would also think that increasing the output would be one aspect of horns, but this is included in both. Increasing the loading of the driver over that of free air increases efficiency and hence the out­put, and concentrating the sound into a certain solid angle increases the output further.

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FUNDAMENTAL THEORYHorn theory, as it has been developed, is based on a series of assumptions and simplifications

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The problem of sound propagation in horns is a complicated one, and has not yet been rigorously solved analytically.

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Initially, it is a three-dimensional prob­lem, but solving the wave equation in 3D is very complicated in all but the most elementary cases.

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Finite horns will transmit sound below their cutoff fre­quency. This can be explained as follows: the horn is an acousti­cal transformer, transforming the high impedance at the throat to a low impedance at the mouth. But this applies only above cutoff. Below cutoff there is no trans­former action, and the horn only adds a mass reactance.

A circular duct with spiral element inside, is an improved Helmholtz resonator.Higher acoustical parameters are achieved when the spiral duct has moreeligible geometrical parameters fitted to the sound wave length.

The acoustic impedanceZ (or sound impedance) is a frequency (f) dependent parameter and is very useful, for example, for describing the behaviour of musical wind instruments. Mathematically, it is the sound pressurep divided by the particle velocityv and the surface area S, through which an acoustic wave of frequency f propagates. If the impedance is calculated for a range of excitation frequencies the result is an impedance curve. Plane, single-frequency traveling waves have acoustic impedance equal to the characteristic impedance divided by the surface area, where the characteristic impedance is the product of longitudinal wave velocity and density of the medium. Acoustic impedance can be expressed in either its constituent units (pressure per velocity per area) or in rayls.

An acoustic transmission line is the acousticanalog of the electrical transmission line, typically thought of as a rigid-walled tube that is long and thin relative to the wavelength of sound present in it

There is a short vertical antenna less than 1/4-wavelength in height. It is loaded at the bottom end with a single-layer solenoid-wound coil. The top section is a vertical rod or wire. Both the coil and rod are considered to be transmission lines.

The input impedance of the rod terminates the coil and is calculated. The input impedance of the coil, the antenna feed-point, is also calculated.

The distributed capacitance of the coil is that of a cylinder in space with the same length and diameter as the coil.

The distributed inductance of the coil is that of a cylinder plus the inductance due to the turns on the coil itself.

The loss resistance of both sections of the antenna includes conductor resistance and radiation resistance.

Program Operating Notes
The antenna is usually used in its resonant condition. The program analyses behaviour at any test frequency.

When there is no rod the antenna is just a close-wound helix with an electrical length of 1/4-wavelength. (Set rod length and diameter to zero).
To resonate the helix, vary test frequency until its electrical length is 90 degrees, or until the coil's input impedance is purely resistive, jXin = 0.

The antenna can be resonated to a particular frequency by varying the number of coil turns. But remember that the number of coil turns also affects things such as wire diameter, wire length and electrical parameters as well as resonant F.

In practice, to resonate to a particular frequency, it is usual to prune the length of the rod or antenna wire. The program can simulate this.

The velocity of light is 300 metres per microsecond.

So, why does the wire or rod need to be pruned (shortened) to be smaller than 1/4 wavelength of the targeted frequency?
The inductance of the coil itself !

In using the program I would enter the speed of sound as the speed of light: 344m/s at 20 C

The resonant condition is when the feed-point reactance, jXin, is at or very near to zero ohms.

Cutoff frequency?

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You can check accuracy of calculations by setting F = 30 MHz and entering rod length to 2500 mm which is 1/4-wavelength at that frequency. The input resistance is the resultant of radiation resistance plus wire loss resistance. Similar calculations are made to determine the feed-point input resistance.

In general, calculating accuracy is good enough for the purpose intended.
The coil's free-space resonant frequency is not the same as it is when mounted vertically above a ground plane and when connected to the rod.
When the antenna is in a quarter-wave resonant condition, note that the sum of the rod and coil phase-shift angles differs considerably from 90 degrees.

Operation of the program at frequencies greater than 1/4-wave resonance has not been checked and is unreliable.

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Winding pitch is coil length divided by the number of turns. Check that calculated wire diameter does not exceed winding pitch or is not too small.

If too small increase diameter/pitch ratio.

To simplify calculations the program neglects "end effect" which results in the resonant length of transmission lines and antenna wires being somewhat shorter than their actual length in wavelengths. In the present context the effect is important only when conductor diameter approaches or exceeds its length. A conductor behaves as if its length is greater than its actual length.

Run this Program from the Web or Download and Run it from Your Computer

This program is self-contained and ready to use. It does not require installation. Click this link CoilLine then click Open to run from the web or Save to save the program to your hard drive. If you save it to your hard drive, double-click the file name from Windows Explorer (Right-click Start then left-click Explore to start Windows Explorer) and it will run.

Personally, I see nothing in conventional Electro-Acoustical theory to disclude the possibility that a spiral transmission line could create an acoustrical inductance (and therefore become an impedance transformer itself, like a horn) and therefor reduce the necessary size of an enclosure modeled so as to be tuned to a certain long wave frequency.

Can those who expound the view that a spiral configuration introduces nothing positive to a low frequency loudspeaker enclosure (Especially concerning size reduction) cite any references in particular to refute such a theory?

Personally, I see nothing in conventional Electro-Acoustical theory to disclude the possibility that a spiral transmission line could create an acoustrical inductance (and therefore become an impedance transformer itself, like a horn) and therefor reduce the necessary size of an enclosure modeled so as to be tuned to a certain long wave frequency.

Can those who expound the view that a spiral configuration introduces nothing positive to a low frequency loudspeaker enclosure (Especially concerning size reduction) cite any references in particular to refute such a theory?

No reference is required to refute it, just a little common sense and logic.

As far as the question of magnetic flux, which is a form of energy createrd by the mechanical action resulting from a wave being induced into a spiral shape. This is energy, correct?

In an airless duct one spiral introduced into a duct resulted in a significant spl level of the tuned frequency resonance.

Can we agree that a mechanical force of inductance was introduced as a result of the spiral?

Looking at figure five of the Lap paper (Not the pdf powerpoint presentation), I would disregard the duct and consider the shape of the spiral.

First, I would wonder if a horn resp designed tapped horn would benifet from the added inducted of building the enclosure exactly acording to the given program measurements, but built in such a way that the enclosure was a quarter wavelength in length. Consider a Tuba stretched out with one spiral.

Since a tapped horn could not be modeled in such a physical design, I would consider the following possibilities:

1.) A push pull spiral tapped horn design with a driver at each end being fed at the mouth from the other driver.

First,

A.) Wouldn't our hypothetical enclosure enjoy the encreased inductance/energy transfer from the two spirals as well as the push pull design?

B.) Assuming the above design uses the same dimensions as two hornresp designed spiral/boxes, shouldn't the spl increase be above those measured in a similar box without the spirals?

C.) Would our box our box offer increased output over the two tapped horns using the same drivers?

D.) Since a push-pull speaker arrangement is said to offer a reduction in box size by as much as half, (though I realize that we arent talking about a true push-pull design here in that it isn't a vented ported box, such as in a 6th level bandpass), would it not offer some inductance in addition to the two spirals?

Then, if the above holds true, shouldn't one be able to at least model a push pull type tapped horn within a spiral duct with at least the same SPL LF level over a single tapped horn in a significantly reduced space requirement?

Or does introducing a properly designed spiral to a 130 Hz wave create SPL increasing inductance that is not mechanically possible with a 20 Hz wave?

Infrasound Defined[…]Infrasonic research is based upon frequencies of 10.0 Hz or below, to 0.0010 Hz (used in monitoring earthquakes), although the lower limit of infrasonic domain is not strictly defined

The Argent RoomLens is an accessory guaranteed to generate skepticism, curiosity, a little admiration, and just maybe a few doubts about the sanity of the owner. The RoomLens is, according to the manufacturer, a "feedback-controlled modified broadband Helmholtz resonator that damps unwanted room resonances while positively reinforcing and focusing the true sound of the system and the room." Still - and this is not to make light of it at all - the RoomLens appears to be a slim five-foot tower of three plastic tubes connected at the top and the bottom. That is, it is not immediately clear that this is a device that, singly or in groups of three, as it is normally deployed, can affect the sound. However, it becomes clear that Ric Cummins, the clever and articulate designer of the RoomLens, has hit upon an interesting solution to room resonance problems.

Using the same principles that help create a guitar's complex tones, researchers at the University of California, Berkeley, have developed a new material that holds promise for revolutionizing the field of ultrasound imaging.

The substance, dubbed an "ultrasonic metamaterial," responds differently to sound waves than any substance found in nature. Within a decade, the researchers report, the technology they developed to create the material could be used to vastly enhance image resolution of ultrasound, while at the same time allowing for the miniaturization of acoustic devices at any given frequency.

The team, led by Nicholas X. Fang, a professor of mechanical science and engineering at Illinois, successfully focused ultrasound waves through a flat metamaterial lens on a spot roughly half the width of a wavelength at 60.5 kHz using a network of fluid-filled Helmholtz resonators. According to the results, published in the May 15 issue of the journal Physical Review Letters, the acoustic system is analogous to an inductor-capacitor circuit. The transmission channels act as a series of inductors, and the Helmholtz resonators, which Fang describes as cavities that house resonating waves and oscillate at certain sonic frequencies almost as a musical instrument would, act as capacitors.

OK, I know. A new substance, a so called “ultrasonic metamaterial” is the principal involved here, not any deviation from any established scientific law of acoustics.

October 25, 2009The acoustic hyperlens is fashioned from 36 brass fins arranged in the shape of a hand-held fan. Each fin is approximately 20 centimeters long and three millimeters thick. Credit: Courtesy of Xiang Zhang research groupUltrasound and underwater sonar devices could "see" a big improvement thanks to development of the world's first acoustic hyperlens. Created by researchers with the U.S. Department of Energy's Lawrence Berkeley National Laboratory, the acoustic hyperlens provides an eightfold boost in the magnification power of sound-based imaging technologies. Clever physical manipulation of the imaging sound waves enables the hyperlens to resolve details smaller than one sixth the length of the waves themselves, bringing into view much smaller objects and features than can be detected using today's technologies.

</H2>The silly fools! Of course that’s not possible. An object 1/6th the size of a given wavelength is necessarily invisible to that frequency. It’s the law!

I was just reading a few hours ago on some website now closed that acoustics is a subject not investigated in physics anymore, as it is considered that all of the essential physical properties of sound waves were discovered in the nineteenth century!

The first paragraph of that document makes the astonishing observation as follows:

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“Although acoustic horns have been in use for thousands of years, formalhorn design only began approximately 80 years ago with the pioneering e_ortof A. G. Webster. In this dissertation, the improvements to Webster's originalhorn model are reviewed and the lack of analytical progress since Webster isnoted.”

Could it be possible that Webster actually retarded the development of the acoustic horn?

Preposterous, you say. Such an assertion would likely be akin to making the claim that Maxwell retarded the development of the science of electromagnetic theory.

This last post is so far out there that it doesn't make any sense. You seem to have missed the point, and application of everything you linked to. Are you sure you have never posted here under another name?

1) Antennas are quite a bit different from acoustics - they're designed to operate at either a single band, or multiple bands with help from a tuned circuit (i.e. an antenna tuner or phaser). Acoustics are wide-band, they're expected to perform relatively the same over several octaves whereas antennas are not.

2) Your use of the term "inductance" with regard to acoustical waveguides is incorrect. Inductance simply means the store of energy in magnetic form and implies electromotive force. Acoustical waveguides do not exhibit inductance.

OK, I'll bite. Exactly where have I deviated from my "original thread topic" central to any of the three threads (to date) that I have posted here in the Subwoofer Forum?

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This last post is so far out there that it doesn't make any sense.

OK. That may or may not be partly my fault. I say "partly" due to a presumption that you haven't actually pulled the links and read the material referenced by myself in this thread. You can now rebut the presumption or it will stand.

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You seem to have missed the point, and application of everything you linked to.

Yet, it is you who just made the claim that "it doesn't make any sense."
Even so, after about five dozen or so hours of reading and research I'm getting a clearer and clearer picture all the time.

It has relevance to what is called a transverse electromagnet wave which is appearantly intentionally suppressed in physics but available to those learned in antenna theory.

I will shortly be looking into the plausablity that a transverse electromagnetic wave is not actually a reflected wave traveling 90 degrees in phase with a a sine wave but is actually the reverse cycle of a wave traveling in a spiral formation- in essence a standing wave travelling slower than the speed of light.

I''l be soon post here a link to a that thread which I will be posting elsewhere in the interest of expanding this discussion. You are welcome to join in, of course.

I have posted links to all of Tom Danley's posts regarding antenna theory applied to the design of tapped horns (that I could find) that he posted here at diyAudio , if you are interested.

Finally, I invite you to come up with some independant observations by seeing if you can google up an animated gif of a directed sound wave packet of multiple frequencies traveling as one wave together as a unit much slower than the speed of sound, even though the waves are still at sound speed...

Does a directed sound packet actually travel in the form of a double cork screw shaped spiral?

If it's not a spiral but instead a funny shaped sine wave, then maybe you can explain how a multi-frequency directed sound wave packet can be moving in unison as one wave at sound speed velocity yet travel slower than the speed of sound?

The 2D representation I saw looked obvious to me as a spiral. Funny that the physics sites I visited never brought up that explanation.

Come to think of it, I do not recall any explanation of why the packet was traveling slower than sound speed. However, I do seem to remember the observation that the phenomenon was interesting to note, but of no value to physicast.

Say what?

Now i am the one having a little comprehension problem here.

Maybe you can help me make some sense of this...

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Are you sure you have never posted here under another name?

That's an odd question. It seems as if an implication being made that not only am I guilty of some perceived offense, but most likely viewed as a serial offender as well.

But, due process demands that before I be asked to present a defense I must be made to understand the nature of what I am being accused of.

Since I have a hobby of practicing law without a license ***(it's fun to "rattle the cage" of the local crime ring running the courthouse from time to time) I stand upon that precipt now.

Regards,

Dane Metcalfe

*** Charges against Johnny were, as predicted, dismissed despite the best efforts of the lawyer* he got scared and hired.

*One of the local crime lords in the above referenced criminal organization.